Question

When calculated, the two differences given below are equal.

(2x^4-3x^3+2x+4)-(-x^4-3x^3+4x^2+x+3)

5x^4-2x^3+3x^2+3x-4
-(2x^4-2x^3+7x^2+2x-5)
-------------------------

A. True
B. False

Answer 1

Think of stuff like x^4 as being a thing.

So, if you have 5 x^4, you have 5 things.
If you have 2 x^4 you have 2 things.

5 times things minus 2 things leaves you with 3 things.

since the things are x to the forths:

\[5X^{4} -2X^{4}=3X^{4}\]
Understand?

That's a basic principle you need to understand. The next bit is more complicated, but I'm not going to explain as in depth, I'm just going to go through it as if you know what you are doing, since it would take too long to give a really in-depth explanation.


Let's look at \[5x^{4}-2x^{3}+3x^{2}+3x-4 -(2x^{4}-2x^{3}+7x^{2}+2x-5)\]

There are 5 x^4s in the expression on left. There are 2x^4s in the polynomial on the right in parentheses.

When you subtract the polynomial on the right (in parentheses) from the polynomial on the left, what you end up with will have 3x^4s.
\[5x^{4}-2x^{3}+3x^{2}+3x-4 -(2x^{4}-2x^{3}+7x^{2}+2x-5)=3x^{4}+some other stuff\]
... just subtract each piece at a time; do not subtract the whole thing at once. We've dealt with the all the x to the forths piece, so let's move onto the x-cubes.

There are 2 x-cubes on the left and negative 2 x-cubes on the right.

2 x cubes minus negative 2 x cubes equal 4 x cubes

\[5x^{4}-2x^{3}+3x^{2}+3x-4 -(2x^{4}-2x^{3}+7x^{2}+2x-5)=3x^{4}+4x^{3}...\]

there are 3 x squards on the left and 7 x squards on the right. 3 - 7 = -4

\[5x^{4}-2x^{3}+3x^{2}+3x-4 -(2x^{4}-2x^{3}+7x^{2}+2x-5)=3x^{4}+4x^{3}-4x^{2}...\]

just keep going and you eventually get:
\[3x^{4}+4x^{3}-4x^{2}+x+1\]

Now so the second subtraction...
[this one:]

5x^4-2x^3+3x^2+3x-4
-(2x^4-2x^3+7x^2+2x-5)
-------------------------

... and see if you set the same answer. If you do, the answer is A. True, the differences are equal. If you don't, the answer is B. False, the differences are NOT equal.

Answer 2

So the answer?